I've seen worse custody/separation battles than a mum who offers to look after the kids while you're at work.
She has raised a concern for safety issue for the child that can extend to a home environment if not managed properly.
She has given you a perfectly reasonable solution.
I get that you have denigrigation concerns in her care, but honestly, if you guys can be seen to work together and cooperate through this, it is going to work out a lot better for you when you go to court.
I can't express this strongly enough. Suck it up and work together for this, it will look very good for you if you do.
If you can't get your head around letting her look after the child during the 9-5 hours for just this period of time, then quit work or take leave or whatever you need to do to free yourself up.
But don't get into a battle over this. She has provided a solution, you can either take it, or provide another one that both parties can agree on.
She appears to agree or have no choice in you having the child in your care ordinarily this week, so whilst you are technically allowed to do whatever you like, trust me, it's not worth the fall out.
These are testing times and the ones who pass the test are going to be rewarded at the end when the courts see no conflict and cooperation.